Simplify csc(x)tan(x)

Problem

csc(x)*tan(x)

Solution

1. Rewrite the cosecant function in terms of sine using the reciprocal identity csc(x)=1/sin(x)

2. Rewrite the tangent function in terms of sine and cosine using the quotient identity tan(x)=sin(x)/cos(x)

3. Substitute these identities into the original expression:

1/sin(x)⋅sin(x)/cos(x)

4. Cancel the common factor of sin(x) from the numerator and the denominator:

1/cos(x)

5. Apply the reciprocal identity 1/cos(x)=sec(x) to reach the simplest form.

Final Answer

csc(x)*tan(x)=sec(x)

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